On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds
High Energy Physics - Theory
2009-11-07 v1 Quantum Algebra
Abstract
A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane.
Cite
@article{arxiv.hep-th/0206039,
title = {On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds},
author = {V. A. Dolgushev and A. P. Isaev and S. L. Lyakhovich and A. A. Sharapov},
journal= {arXiv preprint arXiv:hep-th/0206039},
year = {2009}
}
Comments
18 pages, no figures